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Page 1: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison

to ANSYS Mechanical results

Dave JohnsonPenn State Erie

9/11/2017 1

Page 2: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

Disk modal and harmonic analyses• Steel disk - 75 mm radius and 3mm radius

center hole, and 0.34 mm thickness

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• 1421 SHELL 181 elements• Modulus = 200,000 Mpa• Poisson’s Ratio = 0.3• Density = 7.85E-9 tonnes/mm3

TOTAL MASS: 0.471E-04 (tonne)

• Support: simply-supported, (no translation: UX = UY = UZ = 0) at the edge of the hole

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Page 3: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

Hand calc for verification and validation of modal analysis results

Reference: Mark’s Standard Handbook for Mechanical Engineers, 8th ed., p. 5-75

• For a flat circular plate – constrained at the center, the “umbrella” mode (zero nodal diameters) is predicted by:

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Where:• E = elastic modulus (N/mm2)• r = plate radius (mm)• g = gravity acceleration (mm/s2)• ν = Poisson’s ratio• t = plate thickness (mm)

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Page 4: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

Hand calc for verification and validation of modal analysis results

*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***

MODE FREQUENCY (HERTZ)FREQUENCY RANGE REQUESTED= 0.00 500.001 31.028364525952 31.156689302753 53.417788778604 79.034945984505 79.04406402341

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~3.2% differenceHand calc vs. FEA

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Modal Analysis Results*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***

MODE FREQUENCY (HERTZ)

FREQUENCY RANGE REQUESTED= 0.00000 500.000

1 31.02836452595

2 31.15668930275

3 53.41778877860

4 79.03494598450

5 79.04406402341

6 183.3880216411

7 183.4157944991

8 298.3216528279

9 322.7271830757

10 322.8378280898

11 336.4477549042

12 336.9226420643

13 496.8088338095

14 497.05947940599/11/2017

In the frequency range of interest, we observe 14 modes: 31 < fn < 497 Hz

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Harmonic Analysis Setup• Method: Mode Superposition• Load (1 N) on keypoint in z-direction at edge (at

3 o’clock position)• use all (14) modes from 0 to 500 Hz,

solve 100 substeps• 0.03 damping ratio

(minimal, structural value)• perform an expansion

pass after the harmonic analysis solution

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Harmonic Analysis ResultsZ-deformation at

node where the harmonic load is applied– Linear vs. Log ?

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Note: the Mode Superposition Solutionused 14 modes (in range 0 – 500 Hz), and

max. amplitude (27.59 mm) occurred @ 30 Hz

Page 8: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

Harmonic Analysis Results - 2Use modes from twice the range of interest,

i.e., 0 – 1000 Hz (26 modes were found)

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Note: the Mode Superposition Solutionused 26 modes (in range 0 – 500 Hz), and

max. amplitude (27.62 mm) occured @ 30 Hz

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Harmonic Analysis Results - 3Used the FULL Method, not Mode Superposition

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Note: the FULL Method Solution, maximumamplitude (33.07 mm) occurred @ 30 Hz

Page 10: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

ANSYS Mechanical ComparisonModal linked to Harmonic (B-C) vs. Harmonic (D & E)

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Structural Steel properties from WB library

Same geometry, constraint, and loading

Similar mesh: 1433/1422 SHELL181 elements

TOTAL MASS = 0.47072E-04 (tonne)

[same as ANSYS Mechanical APDL model]

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ANSYS Mechanical Comparison

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Modal linked to Harmonic (B-C) vs. Harmonic (D & E)

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(Split to make vertex for loading)

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ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)

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Compared to ANSYS Mechanical APDL Results:*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***

MODE FREQUENCY (HERTZ)

FREQUENCY RANGE REQUESTED= 0.00 500.0

1 31.02836452595

2 31.15668930275

3 53.41778877860

4 79.03494598450

5 79.04406402341

6 183.3880216411

7 183.4157944991

8 298.3216528279

9 322.7271830757

10 322.8378280898

11 336.4477549042

12 336.9226420643

13 496.8088338095

14 497.0594794059

Page 13: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)

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Note: (default) uses log scale for Amplitude,Solution used 14 modes (in range 0 – 500 Hz),and max. amplitude (18 mm) occurs @ 30 Hz

Page 14: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object D)

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Note: (default) uses log scale for Amplitude,Solution used 26 modes (in range 0 – 1000 Hz),and max. amplitude (26 mm) occurs @ 35 Hz

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ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object E)

using FULL Method

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NOTE: different damping input under Analysis Settings (α = 11 and β = 2e-5) see next slide, and max. amplitude (18.2 mm) occurs @ 30 Hz

Page 16: ANSYS Mechanical-APDL Harmonic Analysis Example …engr.bd.psu.edu/ansysug/ANSYS M-APDL Harmonic... · ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical

Full Harmonic, Damping Input

For this example:

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From ANSYS Help > Mechanical APDL >Structural Analysis Guide > 1.2.1 Alpha & Beta Damping (Rayleigh Damping)

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Comparing Results

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Comparing Results

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Comparing ResultsMaximum Response occurs at 30 or 35 Hz and

the Next Highest Response occurs at 80 Hz

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Conclusions/Observations• Mechanical (WB) default method for Harmonic

Analysis is Mode Superposition. The ANSYS default method is Full

• Mechanical (WB), Harmonic Analysis without linked Modal Analysis, uses 2x the user-requested frequency range, i.e., requested 0 – 500 Hz, and WB used modes from 0 – 1000 Hz

• Mechanical (WB), default Frequency Response plot format uses a log scale for the y-axis (for the Amplitude)

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Conclusions/ObservationsWhy ?• Does the Full Method

show higher max. values, in general ?

• Is Mechanical MSUP-26 max. value at 35 Hz ?

• Should we care about variations at higher frequencies where the amplitude is much less ?

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finish

/clear

/PREP7

ET,1,SHELL181 ! use 3D 4-node thin shell element

!*

MPTEMP,,,,,,,,

MPTEMP,1,0

MPDATA,EX,1,,200000 ! modulus in MPa

MPDATA,PRXY,1,,0.3 ! Poisson's ratio

MPTEMP,,,,,,,,

MPTEMP,1,0

MPDATA,DENS,1,,7.85e-9 ! density in tonnes/mm^3

sect,1,shell,,

secdata, 0.34,1,0.0,3 ! shell thickness 0.34 mm

secoffset,MID

seccontrol,,,, , , ,

PCIRC,75,3,0,360, ! 75 mm outer radius, 3 mm radius center hole

SMRT,6 ! Smart size for meshing

ESIZE,5,0, ! Global element size

MSHAPE,0,2D !

MSHKEY,0 ! allow "free" meshing

!*

AMESH,all ! create the mesh

FINISH

/SOLU

ANTYPE,2 ! Modal analysis

MODOPT,LANB,50 ! use (default) Block Lanczos method

EQSLV,SPAR

MXPAND,50, , ,0 ! extract & expand up to 50 modes

LUMPM,0

PSTRES,0

!*

MODOPT,LANB,50,0,500, ,OFFbv ! frequency range 0 - 500 Hz

lsel,s,,,5,8,1

DL,all, ,UX, ! constraints on edge of hole

DL,all, ,UY,

DL,all, ,UZ,

lsel,all

solve

save,disk_modal,db

finish

/POST1

set,list

finish

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/SOLU

ANTYPE,3 ! Harmonic Analysis

!*

HROPT,MSUP, , ,0 ! Mode Superposition Method

HROUT,ON

LUMPM,0

!*

HROPT,MSUP,14,1,0 ! use (all) 14 modes from modal analysis

HROUT,ON,OFF,0

!*

FK,1,FZ,1, ! Harmonic load amplitude

HARFRQ,0,500, ! Frequency range

NSUBST,100, ! substep thru freq range

KBC,1 ! step change boundary conditions

!*

ALPHAD,0,

BETAD,0,

DMPRAT,0.03, ! 3% damping ratio

DMPSTR,0,

MDAMP,1, , , , , , ,

!*

solve

finish

save,disk_harmonic,db

/SOLU

!*

EXPASS,1 ! Harmonic Analysis Expansion Pass

NUMEXP,ALL,0,500,1 ! Frequency range

HREXP,ALL,

!*

SOLVE

/POST26 ! Time History Postprocessor

*GET,nn,KP,1,ATTR,NODE

NSOL,2,nn,U,Z,

!*

LINES,200

PRCPLX,1 ! print Amplitude/Phase vs. Real/Imaginary results

/AXLAB,Y,UZ Deformation (mm)

/title, disk harmonic analysis - w/linear y-axis (default)

plvar,2

prvar,2

/GROPT,LOGY,ON

/title, disk harmonic analysis - w/log y-axis to match WB

plvar,2